Question

determine a raiz (x-2)²-x.(x-1)=-x²-8x

Answer 1

(x - 2)² - x.(x-1) = -x² - 8x

x² - 4x + 4 - x² + x = - x² - 8x

x² - x² + x² - 4x + x + 8x + 4 = 0

x² + 5x + 4 = 0

a = 1
b = 5
c = 4

Δ = b² - 4ac
Δ = (5)² - 4.(1).(4)
Δ = 25 - 16
Δ = 9

$x = \dfrac{-b \frac{+}{-} \sqrt{b^2-4ac} }{2a}$

$x = \dfrac{-5 \frac{+}{-} \sqrt{9} }{2}$

$x = \dfrac{-5 \frac{+}{-} 3 }{2}$

$x' = \dfrac{-5 + 3}{2}$

x' = -1

$x" = \dfrac{-5 - 3 }{2}$

x" = -4

S = {-4,-1}